Mr. Integral
Math notes/Calculus III/Double Integrals

Polar Coordinates in Double Integrals — Cheat sheet

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Core rule

x=rcos⁡θ,y=rsin⁡θ,dA=r dr dθ.x=r\cos\theta,\quad y=r\sin\theta,\quad dA=r\,dr\,d\theta.

Watch for

Transform the region, integrand and area element together. Avoid tracing a region more than once.